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October, 2004 Seoul. Topological Structure of Dense Hadronic Matter. V. Vento Universitat de València. Colaborators: Heejung Lee (Universitat de València), Byung-Yung Park (Chungnam Nat’l Univ.), Dong-Pil Min (Seoul Nat’l Univ.) and Mannque Rho(Saclay & Hanyang). Introduction
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October, 2004 Seoul Topological StructureofDense Hadronic Matter V. Vento Universitat de València Colaborators: Heejung Lee (Universitat de València),Byung-Yung Park (Chungnam Nat’l Univ.), Dong-Pil Min (Seoul Nat’l Univ.) and Mannque Rho(Saclay & Hanyang)
Introduction • Dense Skyrmion Matter • Pions in Dense Skyrmion Matter • Sliding Vaccua • Vector Mesons • Ongoing work • Concluding remarks
Relevant degrees of freedom? Effective Theory Dynamics?
QCD Effective Theory Observation
QuantumChromo-Dynamics Effective Theory atzero Temp./Density Effective Theory at finite Temp./Density
Skyrme’s Old Idea 1960, T. H. R. Skyrme
Skyrme’s Old Idea topological soliton U(x) : mapping fromR3-{ }=S3toSU(2)=S3 8 BARYON R ~ 1 f m M ~ 1.5 GeV 1960, T. H. R. Skyrme
2. Dense Skyrmion Matter B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A707 (2002) 381
Two Skyrmions 1960, T. H. R. Skyrme Product Ansatz
Toroidal B=2 Skyrmion 1988, Braaten & Carson, 1995, Leese, Manton & Schroers
Multi-Skyrmion System http://www.damtp.cam.ac.uk/user/hep/research.html#solitons
Simple Cubic Skyrmion Crystal Y x z x LC o y y X z x x 1985, I. Klebanov U(x+LC,y,z) =ty U(x,y,z) ty (E/B)min=1.078 atLC=5.56
Half-Skyrmion Crystal z x LC y X s=-1 s=+1 (Lc/2 above) 1987, A. S. Goldhaber & N. S. Manton U(x+LC,y,z) =tyU(x,y,z)ty + additional symmetry (E/B)min=1.076 at LC=5.56
FCC Skyrmion Crystal Y z x z y o y LF X X x z z z=0 plane z=LF/2 plane 1989, L. Castillejo et al. & M. Kugler et al. Y
Half-Skyrmion CC Y Y z x z y o y LF X X z z x (E/B)min=1.038 at Lf=4.72
<tr(U)> Chiral symmetry restoration in dense matter?
3. Pions in Dense Skyrmion Matter H.-J. Lee, B.-Y. Park, D.-P. Min, M. Rho, V. Vento, Nucl. Phys. A723 (2003) 427; Nucl. Phys. A741 (2004) 161
Chiral Symmetry Restoration p-Nsigma term nuclear matter density pion properties in dense medium?
Chiral symmetry restoration GellMann-Oakes-Renner Relation
pion condensation? GellMann-Oakes-Renner Relation
Deeply Bound Pionic States Yamazaki et al., 1998
pdynamics(r=0) Skyrmion matter Pion fluctuations on top of the skyrmion matter \ + p-skyrmion matter interactions
pdynamics(r=0) \ Wavefunction renormalization constant Z-1
Pseudogap phase? Pion effective mass
Pseudogap? Chiral Symmetry Restoration p fp s U still remains on the Chiral Circle But <U>=0 Zarembo, hep-ph/0104305
4. Sliding Vacuua H.-J. Lee, B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A723 (2003) 427
Skyrme Lagrangian Trace Anomaly of QCD Ellis & Lanik, PLB(1985) Brown-Rho scaling, PRL(1992) mc ~ 720 MeV, fc~240 MeV
V(c) c fc Vacuum (r=0) U=1 c=fc
Naive Estimate E/B=M2(L)C2+M4(L) +Mm(L)C3+V(C)
5. Vector Mesons B.-Y. Park, M. Rho, V. Vento, Nucl. Phys. A736 (2004) 129
Hidden Local Gauge Symmetry HLG Trace Anomaly rho & omega vector mesons dilaton + Vector Meson Dominance
pions, chi, rho and omega KSRF relation : mV=afpg2 2 2 Bando, Kugo, Yamawaki, Phys. Rep. (1988)